Tempered fractional time series model for turbulence in geophysical flows

Meerschaert, Mark M.; Sabzikar, Farzad; Phanikumar, Mantha S.; Zeleke, Aklilu

doi:10.1088/1742-5468/2014/09/p09023

Cited by 79 publications

(58 citation statements)

References 25 publications

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“…It may be worth exploring the properties of the fractional derivatives of the solar wind time series (e.g., Repperger et al, ) to see if they can provide insight into the noninteger high‐frequency power laws observed in the PSDs. Fractional derivatives of the time series are readily calculated using Fourier transforms (Meerschaert et al, ; Tseng et al, ).…”

Section: Discussionmentioning

confidence: 99%

On the Fourier Contribution of Strong Current Sheets to the High‐Frequency Magnetic Power SpectralDensity of the Solar Wind

Borovsky

Burkholder

2020

JGR Space Physics

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The hypothesis is explored that the high‐frequency magnetic spectral power of the solar wind is associated with the spatial profiles of strong current sheets (directional discontinuities) in the solar wind plasma. This hypothesis is based on previous findings about current sheets and the solar wind's magnetic power spectra (1) that the amplitude distribution and waiting time distribution of strong current sheets determines the amplituic composition and the electron strade and spectral slope of the “inertial range” of frequencies and (2) that the thicknesses of strong current sheets in the solar wind determine the breakpoint frequency that ends the inertial range. Solar wind current sheets are collected from the WIND 0.09375‐s and MMS 7.8 × 10−3‐s magnetic data sets, and the current sheets are individually Fourier transformed. At frequencies above the solar wind breakpoint (1) the shape of the magnetic power spectra of the current sheets resembles the shape of the magnetic power spectra of the solar wind and (2) the current sheets occur frequently enough to account for the magnetic power of the solar wind above the breakpoint. This has implications for the physics underlying the high‐frequency magnetic power spectral density of the solar wind, supplementing the energy‐cascade description of the high‐frequency spectrum.

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Section: Discussionmentioning

confidence: 99%

On the Fourier Contribution of Strong Current Sheets to the High‐Frequency Magnetic Power SpectralDensity of the Solar Wind

Borovsky

Burkholder

2020

JGR Space Physics

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“…It was also reported that retention of contaminant particles in river beds and eddy pools causes a power-law trailing edge in the concentration profile, which corresponds to (1) with θ = 0 [26,27]. Hence, the model is of the same form as (5), with the left fractional derivative replaced by the right fractional derivative, and hence can be solved by the same method developed in this paper.…”

Section: Problem Formulationmentioning

confidence: 88%

“…We carry out numerical experiments to investigate the performance of the Petrov-Galerkin finite element method for problem (5). We use a uniform space partition with a mesh size h := 1/N .…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the last few decades fractional differential equations (FDEs) have found increasingly more applications in fluid mechanics [1], anomalous diffusion and acceleration of steep fronts in reaction-diffusion processes [2,3], turbulence in geophysical flows or plasma physics [4][5][6], continuum mechanics [7], as they provide very effective alternatives for modeling complex systems characterized by nonlocal phenomena and long range interactions. However, FDEs present mathematical difficulties that have not been encountered in the context of second-order differential equations.…”

Section: Introductionmentioning

confidence: 99%

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A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations

Wang

Yang

Zhu

2015

Computer Methods in Applied Mechanics and Engineering

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“…C iw/˛O u.w/, along with its inverse, the tempered fractional integral I˛, u.t/, whose Fourier transform is . C iw/ ˛O u.w/ [6,15,16,[18][19][20]. Because of tempering, the Fourier symbol .…”

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confidence: 99%

Tempered fractional differential equation: variational approach

Torres

2017

Math. Meth. Appl. Sci.

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In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: {arrayD−α,λ(D+α,λu(t))=f(t,u(t)),t∈Rarrayu∈Wα,2(R), where α∈(1/2,1), λ>0, double-struckD±α,λu are the left and right tempered fractional derivatives, Wα,2(double-struckR) is the fractional Sobolev spaces, and f∈C(double-struckR×double-struckR,double-struckR). Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd.

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Tempered fractional time series model for turbulence in geophysical flows

Cited by 79 publications

References 25 publications

On the Fourier Contribution of Strong Current Sheets to the High‐Frequency Magnetic Power SpectralDensity of the Solar Wind

On the Fourier Contribution of Strong Current Sheets to the High‐Frequency Magnetic Power SpectralDensity of the Solar Wind

A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations

Tempered fractional differential equation: variational approach

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